Someone wins my giveaway, rejects friend request on steam to give the winner the game.

wait 7 days.

can you send the gift or key by email?

if not, take screenshots and reroll after 7 days.

Try dropping them a line so they know why you are trying to add them.
Be patient, sometimes it may happen that the person is busy enough for the whole week. :)
Tip for the future: put a level limit (even 1) on the GA, so that at least you know that the other person knows how to operate the site. :D
Have a nice day! :)

if thats how you want to deliver the gift, then you can reroll after a week if they dont accept. you could also leave a message on a giveaway they have made stating you are trying to add them.

if you are ok with other ways, you could try the email gift option

yeah....i always send gift throw email and so far never had a problem with that.....it is more than 10 games already

You can send the winner the game via e-mail.